Vehicles of today may include one or more attitude and heading reference systems (AHRS). An AHRS system is commonly viewed as a tri-axial sensor system that is capable of providing real-time orientation and direction information. As a result, such a system is required to be reliable, efficient and accurate. In order to calculate navigation related parameters, an AHRS system typically includes gyroscopes, accelerometers and magnetometers that are capable of sensing and measuring rotation, proper acceleration and magnetic field magnitude, respectively.
Typically, vehicles having an attitude and heading reference system, such as an aircraft having an AHRS, must be periodically calibrated to minimize measurement errors attributed to hardware and/or environmental factors. In order to achieve such calibration, alternative techniques may be employed to obtain redundant measurements that can be used for comparative purposes. Typically, these redundant measurements rely on the use of vehicle probes (e.g., sensors) capable of measuring variables such as static air temperature, static air pressure, variable/dynamic air pressure and others. However, in many instances, the required vehicle probes may malfunction, become inoperative, be inaccessible, or be absent thus hindering the collection of the desired measurements. For example, a MEMS-based AHRS may rely on measurements produced by one or more MEMS-based gyroscopes to provide attitude and heading measurements. These MEMS-based gyroscopes tend to suffer from a long term random walk (i.e., bias). Accordingly, a second and independent source of measurement may be employed to provide or augment attitude and heading measurements. In turn, these independent attitude and heading measurements are used to correct the gyro bias on a periodic basis.
Sources of these independent attitude and heading measurements include accelerometers and magnetometers. Accelerometers and other such sensors, however, are susceptible to forces other than gravity (e.g., centripetal forces induced by vehicle turns), which tend to introduce additional errors. To further compensate for such outside forces, a dynamic model is used. For example, in flight systems, the dynamic model assumes a coordinated turn and employs the equation:
      θ    =                  tan                  -          1                    ⁡              (                              T            ⁢                                                  ⁢            A            ⁢                                                  ⁢                          S              ·              T                        ⁢                                                  ⁢                          R              ·              K                                g                )              ,where: θ is Bank Angle, TAS is True Airspeed, TR is Turn Rate, K is a scaling factor and g is Gravity. In turn, the models of the affected sensor systems are augmented by the bank angle calculation from the dynamic model. For example, the sensor (e.g., accelerometer, magnetometer) measurement model may be augmented by the bank angle θ computed from the dynamic model.
As can be seen from the dynamic model equation
      θ    =                  tan                  -          1                    ⁡              (                              T            ⁢                                                  ⁢            A            ⁢                                                  ⁢                          S              ·              T                        ⁢                                                  ⁢                          R              ·              K                                g                )              ,a measurement of true airspeed (TAS) is required to compute vehicle bank angle θ. True airspeed (TAS) itself is a function of dynamic pressure, static pressure, and static air temperature and can be expressed according to the following relationship:
            T      ⁢                          ⁢      A      ⁢                          ⁢      S        =          661.47      ⁢                                                  5              ⁢                                                          ⁢              T                        288.15                    ⁡                      [                                                            (                                                                                    q                        c                                            P                                        +                    1                                    )                                                  2                  7                                            -              1                        ]                                ,where: T is static air temperature, qc is dynamic pressure, and P is static pressure.
Typically, an AHRS would rely on true airspeed calculations from an air data computer. However, in an Air Data Attitude Heading Reference System (ADAHRS), the true airspeed is calculated internally by interfacing with the aircraft probes. In each case, probes measure the dynamic pressure, static pressure, and static air temperature. For example, most air data computers interface with the aircraft pitot probe for measurement of dynamic pressure, static probe for measurement of static pressure, and static air temperature probe for measurement of static air temperature.
In situations where there are no accessible outside temperature probes or the temperature probe has failed, default/standard models may be used to provide a temperature estimate. For example, an International Standard Atmosphere (ISA) temperature model of the earth can be used to estimate the outside static air temperature based on the current altitude, where a 20° C. temperature at sea level is assumed. Because this is a default model meant to provide an approximation, however, this estimated temperature may not be reflective of actual conditions, thereby leading to inaccuracies in the TAS calculation.
Because sensors (e.g., temperature, pressure, etc.) have been known to fail, become unavailable, or otherwise cease to provide measurements, there is a need to provide for an improved estimate of these measurements in the event of such failure or other absence. Similarly, there is also a need to provide an estimate of true airspeed in the event of similar or other sensor failures that are used to calculate true airspeed (TAS), such as pressure probes.